Flow meter using an expanded tube section and sensitive differential pressure measurement

ABSTRACT

A method and apparatus for measuring the flow rate of a fluid within tubing disposed within a downhole wellbore. The present invention provides an inverse Venturi meter inserted within tubing with an enlarged inner diameter portion. Pressure differential is measured between the enlarged inner diameter portion and another portion of the inverse Venturi meter. Flow rate is determined from the pressure differential and the density of the fluid.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of co-pending U.S. patent applicationSer. No. 10/647,014, filed Aug. 22, 2003 now U.S. Pat. No. 6,910,388.The aforementioned related patent application is herein incorporated byreference in its entirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

Embodiments of the present invention generally relate to downholeproduction operations conducted within a wellbore. More specifically,embodiments of the present invention relate to measuring flow ratesdownhole.

2. Description of the Related Art

In the drilling of oil and gas wells, a wellbore is formed using a drillbit that is urged downwardly at a lower end of a drill string. When thewell is drilled to a first designated depth, a first string of casing isrun into the wellbore. The first string of casing is hung from thesurface, and then cement is circulated into the annulus behind thecasing. Typically, the well is drilled to a second designated depthafter the first string of casing is set in the wellbore. A second stringof casing, or liner, is run into the wellbore to the second designateddepth. This process may be repeated with additional liner strings untilthe well has been drilled to total depth. In this manner, wells aretypically formed with two or more strings of casing having anever-decreasing diameter.

After a well has been drilled, it is desirable to provide a flow pathfor hydrocarbons from the surrounding formation into the newly formedwellbore to allow for hydrocarbon production. Therefore, after all ofthe casing has been set, perforations are shot through a wall of theliner string at a depth which equates to the anticipated depth ofhydrocarbons. Alternatively, a liner having pre-formed slots may be runinto the hole as casing. Alternatively still, a lower portion of thewellbore may remain uncased so that the formation and fluids residingtherein remain exposed to the wellbore.

During the life of a producing hydrocarbon well, real-time, downholeflow data regarding the flow rate of the hydrocarbons from the formationis of significant value for production optimization. The flow rateinformation is especially useful in allocating production fromindividual production zones, as well as identifying which portions ofthe well are contributing to hydrocarbon flow. Flow rate data may alsoprove useful in locating a problem area within the well duringproduction. Real-time flow data conducted during production ofhydrocarbons within a well allows determination of flow characteristicsof the hydrocarbons without need for intervention. Furthermore,real-time downhole flow data may reduce the need for surface well testsand associated equipment, such as a surface test separator, therebyreducing production costs.

Downhole flow rate data is often gathered by use of a Venturi meter. TheVenturi meter is used to measure differential pressure of thehydrocarbon fluid across a constricted cross-sectional area portion ofthe Venturi meter, then the differential pressure is correlated with aknown density of the hydrocarbon fluid to determine flow rate of thehydrocarbon mixture. FIG. 1 depicts a typical Venturi meter 9. TheVenturi meter 9 is typically inserted into a production tubing string 8at the point at which the flow rate data is desired to be obtained.Hydrocarbon fluid flow F exists through the production tubing string 8,which includes the Venturi meter 9, as shown in FIG. 1. The Venturimeter 9 has an inner diameter A at an end (point A), which iscommensurate with the inner diameter of the production tubing string 8,then the inner diameter decreases at an angle X to an inner diameter B(at point B). Diameter B, the most constricted portion of the Venturimeter 9 typically termed the “throat”, is downstream according to fluidflow F from the end having diameter A. The Venturi meter 9 thenincreases in inner diameter downstream from diameter B as the innerdiameter increases at angle Y to an inner diameter C (typicallyapproximately equal to A) again commensurate with the production tubingstring 8 inner diameter at an opposite end of the Venturi meter 9.

Angle X, which typically ranges from 15–20 degrees, is usually greaterthan angle Y, which typically ranges from 5–7 degrees. In this way, thefluid F is accelerated by passage through the converging cone of angleX, then the fluid F is retarded in the cone increasing by the smallerangle Y. The pressure of the fluid F is measured at diameter A at theupstream end of the Venturi meter 9, and the pressure of the fluid F isalso measured at diameter B of the throat of the Venturi meter 9, andthe difference in pressures is used along with density to determine theflow rate of the hydrocarbon fluid F through the Venturi meter 9.

In conventional Venturi meters used in downhole applications, diameter Ais larger than diameter B. Typically, diameter A is much larger thandiameter B to ensure a large differential pressure between points A andB. This large differential pressure is often required because theequipment typically used to measure the difference in pressure betweenthe fluid F at diameter A and the fluid F at diameter B is not sensitiveenough to detect small differential pressures between fluid F flowingthrough diameter A and through diameter B. The extent of convergence ofthe inner diameter of the Venturi meter typically required to create ameasurable differential pressure significantly reduces the availablecross-sectional area through the production tubing string 8 at diameterB. Reducing the cross-sectional area of the production tubing string 8to any extent to obtain differential pressure measurements isdisadvantageous because the available area through which hydrocarbonsmay be produced to the surface is reduced, thus affecting productionrates and, consequently, reducing profitability of the hydrocarbon well.Furthermore, reducing the cross-sectional area of the production tubingstring with the currently used Venturi meter limits the outer diameterof downhole tools which may be utilized during production and/orintervention operations during the life of the well, possibly preventingthe use of a necessary or desired downhole tool.

Venturi flow meters suffer from additional disadvantages to restrictedaccess below the device (which may prevent the running of tools belowthe device) and reduced hydrocarbon flow rate. Venturi meters currentlyused cause significant pressure loss due to the restrictive nature ofthe devices. Further, because these devices restrict flow of the mixturewithin the tubing string, loss of calibration is likely due to erosionand/or accumulation of deposits (e.g., of wax, asphaltenes, etc.). Thesedisadvantages may be compounded by poor resolution and accuracy ofpressure sensors used to measure the pressure differences. Overcomingthe poor resolution and accuracy may require the use of high contractionratio (e.g., more restrictive) Venturi meters, thus furtherdisadvantageously restricting the available cross-sectional area forhydrocarbon fluid flow and lowering downhole tools.

Therefore, it is desirable to provide a downhole flow meter withinproduction tubing and other tubing strings through which fluid flowsdownhole within a wellbore which does not restrict the cross-sectionalarea available for production of hydrocarbons through the productiontubing or fluid flow through other tubing. It is desirable to provide adownhole flow meter that measures flow rates within production tubingwithout causing a restriction in production tubing diameter. It isfurther desirable to provide a method of measuring downhole flow rate ofhydrocarbons without restricting production of hydrocarbons or the typesof tools which may be used downhole below the flow meter.

SUMMARY OF THE INVENTION

The present invention generally provides apparatus and methods fordetermining a flow rate of fluid within a pipe. In one aspect, thepresent invention includes a method of determining a flow rate of fluidflowing within a pipe, comprising providing a pipe, at least a portionof the pipe having a larger inner diameter than a nominal inner diameterof the pipe, wherein the pipe diverges from the nominal inner diameterof the pipe to the larger inner diameter of the pipe in the direction offluid flow; measuring a differential pressure between at least twolocations along the pipe, at least one location positioned in theportion having an inner diameter greater than the nominal inner diameterof the pipe; and determining a flow rate for the fluid based on themeasured differential pressure. In another aspect, the present inventionincludes a method for determining the flow rate of fluid throughdownhole tubing, comprising providing an enlarged inner diameter portionof the downhole tubing disposed upstream of a remaining portion of thetubing; measuring a pressure differential between the enlarged innerdiameter portion of the tubing and the remaining portion of the tubing;and determining the flow rate of the fluid using the pressuredifferential.

Further, the present invention provides in another aspect an apparatusfor measuring a flow rate of a fluid flowing in a pipe disposed in awellbore, comprising at least one differential pressure sensor disposedalong the pipe across two locations for sensing differential pressurealong the pipe, wherein at least one of the locations is at an enlargedinner diameter portion of the pipe, and wherein the pipe diverges from anominal inner diameter of the pipe to the enlarged inner diameter of thepipe in the direction of fluid flow; processing equipment for convertingthe differential pressure to flow rate data; and one or moretransmission lines for communicating differential pressure informationfrom the at least one differential pressure sensor to the processingequipment.

In yet another aspect, the present invention includes an apparatus formeasuring flow rate of fluid within a wellbore, comprising a tubingstring having a diverging inner diameter portion positioned upstream ofa section of the tubing string, wherein the tubing string is disposedwithin the wellbore; and a differential pressure sensor disposed on thetubing string and the diverging inner diameter portion for measuring adifference between fluid pressure in the tubing string and fluidpressure in the diverging inner diameter portion. Finally, in yetanother aspect, the present invention provides a flow meter for use inmeasuring fluid flow within a downhole wellbore, comprising first andsecond portions, each having substantially the same inner diameter; anda middle portion, an inner diameter of the middle portion divergingoutward toward the wellbore from the first and second portions, whereina difference in fluid pressure is measurable between the middle portionand the first or second portion.

BRIEF DESCRIPTION OF THE DRAWINGS

So that the manner in which the above recited features of the presentinvention can be understood in detail, a more particular description ofthe invention, briefly summarized above, may be had by reference toembodiments, some of which are illustrated in the appended drawings. Itis to be noted, however, that the appended drawings illustrate onlytypical embodiments of this invention and are therefore not to beconsidered limiting of its scope, for the invention may admit to otherequally effective embodiments.

FIG. 1 is a sectional view of a typical downhole Venturi meter insertedwithin a string of production tubing.

FIG. 2 is a sectional view of an exemplary flow rate measurement systemincluding a flow meter according to an embodiment of the presentinvention. A differential pressure sensor measures pressure across theflow meter.

FIG. 3 is a sectional view of an alternate embodiment of the flow ratemeasurement system of the present invention. Two absolute pressuresensors measure pressure at two locations across the flow meter.

FIG. 4 is a sectional view of an alternate embodiment of the flow ratemeasurement system of the present invention. A fiber optic differentialpressure sensor measures pressure across a flow meter according to thepresent invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

As described below, the present invention involves an “inverse Venturimeter” or “inverse Venturi flow meter”, meaning that instead of thetypical constricted, converging inner diameter portion at the throatcharacteristic of typical Venturi meters, the inverse Venturi meterincludes a flow meter with an enlarged, diverging inner diameter portionat the “throat”. By utilizing an ultra-sensitive differential pressuremeasurement device along with an inverse Venturi meter, the presentinvention allows downhole flow rate measurements to be obtained withoutrestricting the inner diameter of production tubing. The presentinvention thus advantageously increases the cross-sectional areaavailable for flow of hydrocarbon fluid through the production tubingduring production operations or for the flow of other fluid duringcompletion or intervention operations. Furthermore, the presentinvention increases the available diameter through which downhole toolsmay be lowered within the tubing disposed in a wellbore when using aVenturi meter.

As used herein, the terms “tubing string” and “pipe” refer to anyconduit for carrying fluid. Although the description below relates to aproduction tubing string, a tubing string utilized for any purpose,including intervention and completion operations, may employ theapparatus of the present invention to determine fluid flow rate. Fluidis defined as a liquid or a gas or a mixture of liquid or gas. Tofacilitate understanding, embodiments are described below in referenceto measuring hydrocarbon fluid parameters, but it is contemplated thatany fluid may be measured by the below-described apparatus and methods.

FIG. 2 shows an exemplary downhole flow rate measurement system 55 forobtaining measurements of flow rates of fluid F produced from asurrounding formation 5. (The flow rate measurement system 55 may alsobe used to measure the flow rates of other types of fluids flowingthrough a pipe for any purpose.) A flow meter (also “inverse Venturimeter”) 60 is disposed within a production tubing string 15, preferablythreadedly connected at each end to a portion of the production tubingstring 15, so that the inverse Venturi meter 60 is in fluidcommunication with the production tubing string 15. Fluid F flows fromdownhole within a production zone (not shown) in the formation 5 to asurface 40 of a wellbore 20, as indicated by the arrow shown in FIG. 2.

As shown in FIG. 2, the inverse Venturi meter 60 includes atubular-shaped body with four portions 60A, 60B, 60C, and 60D. The lowerportion 60D has a diameter A which is capable of mating with the portionof the tubing string 15 below the inverse Venturi meter 60. The lowermiddle portion 60C of the inverse Venturi meter 60, located above thelower portion 60D, gradually increases in diameter at a divergence angleX to a diameter B which exists at a throat 61 of the inverse Venturimeter 60. The throat 61 represents the maximum diameter B of the inverseVenturi meter 60. The diameter of the inverse Venturi meter 60 divergesoutward from diameter A (the nominal pipe diameter) to the throat 61.

Now referring to the remaining portions 60A and 60B of the inverseVenturi meter 60, the upper portion 60A is of a diameter C which iscapable of mating with the portion of the tubing string 15 above theinverse Venturi meter 60. Located below the upper portion 60A is theupper middle portion 60B. In the upper middle portion 60B, the diameterof the inverse Venturi meter 60 increases in diameter at a divergenceangle Y until reaching the throat 61 at diameter B. In addition torepresenting the maximum diameter B of the Venturi meter 60, the throat61 also is the point at which the upper middle portion 60B and the lowermiddle portion 60C meet.

The increase in diameter from diameter A and/or C to diameter B isminimal in comparison to the diameters A and C, in one embodiment mostpreferably an increase in diameter of approximately 0.25 inches. Thegoal is to maximize the available area within the production tubing 15and the inverse Venturi meter 60 with respect to the inner diameter ofthe wellbore 20. Accordingly, taking into account the available diameterwithin the wellbore 20, an increase in diameter of the tubing string 15at diameter B which is too large would unnecessarily restrict the innerdiameter of the remainder of the tubing string 15 with respect to thesize of the wellbore 20, decreasing hydrocarbon fluid flow and the areathrough which tools may be lowered into the production tubing 15.Exemplary, but not limiting, embodiments have a nominal diameter Aand/or C of 3.5 inches, 4.5 inches, or 5.5 inches, with a throat 61diameter B of 3.7, 4.7, or 5.6 inches, respectively, depending upon thediameter of the ends of the production tubing string 15 with which theinverse Venturi meter 60 is intended to mate. Most preferably, in anembodiment of the present invention, diameter A and/or C is about 3.5inches, while diameter B is about 3.75 inches. Diameter A and diameter Cmay be the same or different diameters, depending upon the diameter ofthe ends of the production tubing string 15 with which the inverseVenturi meter 60 is intended to mate. Angles X and Y may be any angleswhich produce a measurable differential pressure between the throat 61and diameter A. The angles X and Y and the lengths of the divergingsections 60B and 60C are determined such that a satisfactory Reynoldsnumber is achieved in the flow range of interest. The angles X and Yshown in FIG. 2 are exaggerated for illustration purposes; ideally,although not limiting the range of angles contemplated, the angles aresmall to provide the maximum tubing string 15 diameter and diameters Aand/or C through which tools may be inserted and through which fluid Fmay flow (taking into account the size of the wellbore 20).

Disposed on the outer diameter of the inverse Venturi meter 60 andcoupled to the pipe is a differential pressure sensor 50. Thedifferential pressure sensor 50 has pressure ports leading to the throat61 and to diameter A (or diameter C) so that it can detect thedifference in pressure between diameter A (or diameter C) and the throat61. The differential pressure sensor 50 may include any suitable highresolution or ultra-sensitive differential pressure sensor, including afiber optic or optical differential pressure sensor (see FIG. 4). Asuitable differential pressure sensor 50 is capable of measuring adifference in pressure between fluid F flowing through diameter A andfluid flowing through the throat 61.

Operatively connected to the differential pressure sensor 50 is at leastone signal line or cable 36 or optical waveguides. The signal line 36runs outside the tubing string 15 to the surface 40, where it connectsat the opposite end to surface control circuitry 30. The controlcircuitry 30 may include any suitable circuitry responsive to signalsgenerated by the differential pressure sensor 50. As illustrated, thecontrol circuitry 30 includes signal interface circuitry 32 and logiccircuitry 34. The signal interface circuitry 32 may include any suitablecircuitry to receive signals from the differential pressure sensor 50via one or more signal lines 36 and properly condition the signals(e.g., convert the signals to a format readable by the logic circuitry34).

The logic circuitry 34 may include any suitable circuitry and processingequipment necessary to perform operations described herein. For example,the logic circuitry 34 may include any combination of dedicatedprocessors, dedicated computers, embedded controllers, general purposecomputers, programmable logic controllers, and the like. Accordingly,the logic circuitry 34 may be configured to perform operations describedherein by standard programming means (e.g., executable software and/orfirmware).

The signals generated by the inverse Venturi meter 60 may be anysuitable combination of signals, such as electrical signals, opticalsignals, or pneumatic signals. Accordingly, the signal lines 36 may beany combination of signal bearing lines, such as electrically conductivelines, optical fibers, or pneumatic lines. Of course, an exact numberand type of signal lines 36 will depend on a specific implementation ofthe inverse Venturi meter 60.

In operation, the inverse Venturi meter 60 is inserted into theproduction tubing 15 as shown in FIG. 2. The production tubing 15 alongwith the inverse Venturi meter 60 is lowered into the drilled outwellbore 20. The signal line(s) 36 may be connected to the differentialpressure sensor 50 prior to or after inserting the inverse Venturi meter60 into the wellbore 20. After flow F is introduced into the tubingstring 15 from the formation 5, it flows upward into the inverse Venturimeter 60. The differential pressure sensor 50 measures the pressuredifference from diameter A to the throat 61 in real time as the fluid Fpasses the throat 61.

The pressure difference from the throat 61 to diameter A is relayed tothe surface 40 through the signal line(s) 36. The control circuitry 30then converts the signal from the signal line(s) to meaningful flow ratedata. To obtain the flow rate of the fluid F, the density of the fluidmust be known. “Density” generally refers to volumetric density and isdefined as a mass of a fluid contained within a volume divided by thevolume. Density of the fluid F may be obtained by any known method.Suitable methods include, but are not limited to, measuring a density ofthe fluid F after it reaches the surface by known methods as well asmeasuring a density of the fluid downhole by, for example, including anabsolute pressure sensor and an absolute temperature sensor along theinverse Venturi meter 60 and coupling the sensors to the pipe(formulating a density meter) and including suitable surface processingequipment as described in co-pending U.S. patent application Ser. No.10/348,040, entitled “Non-Intrusive Multiphase Flow Meter,” filed onJan. 21, 2003, which is herein incorporated by reference in itsentirety.

The control circuitry 30 uses the density and the pressure differentialto determine the flow rate of the fluid F. The equation utilized todetermine the flow rate of the fluid F of a given density with A and Bis the following:

${Q = \sqrt{\frac{2}{\rho} \times {DP} \times \frac{\pi}{4} \times \left\lbrack {D_{B}^{2} - D_{A}^{2}} \right\rbrack}},$where q=flow rate, ρ=density of the fluid F, DP=minimum measurablepressure differential, D_(B)=the largest diameter or the expandeddiameter of the inverse Venturi meter 60 (diameter B at the throat 61),and D_(A)=the smaller diameter of the inverse Venturi meter 60 upstreamof the throat 61 (diameter A, or the nominal pipe size of the Venturimeter tubing). D_(A) may also be the smaller diameter C (or nominal pipesize) of the inverse Venturi meter 60 downstream of the throat 61,depending upon at which point on the inverse Venturi meter 60 thedifferential pressure sensor is located. When using the most preferableembodiment of the inverse Venturi meter 60 mentioned above, which ismerely exemplary and not limiting, assuming no elevation of the inverseVenturi meter 60 and a fluid density of 0.85 g/cm³, the lowestmeasurable flow rate would be 0.08 feet/second for a differentialpressure sensor 50 having a minimum differential pressure, ordifferential pressure resolution, of 0.001 psid.

FIG. 3 shows a further alternate embodiment of the present invention.Like parts are labeled with like numbers to FIG. 2. Instead of a singledifferential pressure sensor 50, an upper absolute pressure sensor 70 islocated at the throat 61, while a lower absolute pressure sensor 75 islocated at portion 60D of the inverse Venturi meter having diameter A.The sensors 75 and 70 are coupled to the pipe. The upper and lowerabsolute pressure sensors 70 and 75 are high resolution sensors so thatpressure may be detected at each location to a high precision so that adifferential pressure results when the pressures are subtracted from oneanother at the surface. The upper pressure sensor 70 is connected by asignal line or cable 71 or optical waveguides to the control circuitry30, and the lower pressure sensor 75 is likewise connected by a signalline or cable 72 or optical waveguides to the control circuitry 30.Alternatively, the sensors 70 and 75 may be connected to a single commonsignal line or cable (multiplexed).

In operation, each of the upper pressure sensor 70 and the lowerpressure sensor 75 determine a pressure of the fluid F at locations nearthe throat 61 as well as near the portion 60D of diameter A. The upperpressure sensor 70 sends the pressure information from its location witha signal through signal line 71. The lower pressure sensor 75 sends thepressure information from its location with a signal through signal line72. The control circuitry 30 then subtracts the two pressuremeasurements to determine the differential pressure and uses the densityof the fluid with the determined differential pressure to calculate flowrate at a location using the same equation disclosed above in relationto FIG. 2.

Regardless of the particular arrangement, the differential pressuresensors 50 or absolute pressure sensors 70 and 75 may be any combinationof suitable sensors with sufficient sensitivity to achieve the desiredresolution (preferably 0.001 psid). As an example, the pressure sensors50, 70, 75 may be any suitable type of ultra-sensitive strain sensors,quartz sensors, piezoelectric sensors, etc. Due to harsh operatingconditions (e.g., elevated temperatures, pressures, mechanical shock,and vibration) that may exist downhole, however, accuracy and resolutionof conventional electronic sensors may degrade over time.

Fiber optic sensors or optical sensors offer one alternative toconventional electronic sensors. Typically, fiber optic sensors have nodownhole electronics or moving parts and, therefore, may be exposed toharsh downhole operating conditions without the typical loss ofperformance exhibited by electronic sensors. Additionally, fiber opticsensors are more sensitive than traditional sensors, which allowsdetection of the relatively small pressure differential produced by theinverse Venturi meter 60 of the present invention. Accordingly, for someembodiments, one or more of the sensors 50, 70, 75 utilized in theinverse Venturi meter 60 may be fiber optic sensors.

FIG. 4 shows an alternate embodiment of the present invention using afiber optic sensor. Like parts in FIG. 4 are labeled with like numbersto FIG. 2. In this embodiment, the differential pressure sensor 50 is afiber optic sensor, which satisfies the requirement of a high resolutiondifferential pressure sensor 50. The signal line(s) 36 is a fiber opticcable or line, and the fiber optic or optical cable 36 is connected atone end to the fiber optic sensor 50 and at the other end to controlcircuitry 130, which includes optical signal processing equipment 135and logic 134 as well as a light source 133. The control circuitry 130converts the signal relayed through the fiber optic line 36 tomeaningful flow rate data and delivers signal light through the fiberoptic line 36.

For some embodiments, the fiber optic sensors may utilizestrain-sensitive Bragg gratings (not shown) formed in a core of one ormore optical fibers or other wave guide material (not shown) connectedto or in the signal line 36. A fiber optic sensor is utilized as thedifferential pressure sensor 50 and therefore becomes a fiber opticdifferential pressure sensor. Bragg grating-based sensors are suitablefor use in very hostile and remote environments, such as found downholein the wellbore 20.

As illustrated, to interface with fiber optic sensors, the controlcircuitry 130 includes a broadband light source 133, such as an edgeemitting light emitting diode (EELED) or an Erbium ASE light source, andappropriate equipment for delivery of signal light to the Bragg gratingsformed within the core of the optical fibers. Additionally, the controlcircuitry 130 includes appropriate optical signal processing equipment135 for analyzing the return signals (reflected light) from the Bragggratings and converting the return signals into data compatible withdata produced by the logic circuitry 134.

The operation of the flow measurement system of FIG. 4 is the same asthe operation of the flow measurement system of FIG. 2, except that thedifferential pressure sensor or fiber optic sensor 50 sends a fiberoptic signal through the fiber optic cable 36 to the surface forprocessing with the optical signal processing equipment 135. The opticalsignal processing equipment 135 analyzes the return signals (reflectedlight) from the Bragg gratings and converts the return signals intosignals compatible with the logic circuitry 134.

In a further alternate embodiment of the present invention, absolutepressure sensors 70 and 75 of FIG. 3 may be fiber optic or opticalsensors, which send a signal through the fiber optic cable 36 of FIG. 4to the control circuitry 130 for surface processing. In this embodiment,the control circuitry 130 may include a broadband light source 133,logic circuitry 134, and appropriate optical signal processing equipment135, as described above in relation to FIG. 4. The pressure readingsfrom fiber optic sensors 70 and 75 at the two locations are subtractedfrom one another and placed into the equation above stated to gain flowrate data. As in FIG. 3, the sensors 70 and 75 may alternatively beconnected to a single common signal line or cable.

Whether fiber optic sensors are utilized as the differential pressuresensor 50 or the absolute pressure sensors 70 and 75, depending on aspecific arrangement, the fiber optic sensors may be distributed on acommon one of the fibers or distributed among multiple fibers. Thefibers may be connected to other sensors (e.g., further downhole),terminated, or connected back to the control circuitry 130. Accordingly,while not shown, the inverse Venturi meter 60 and/or production tubingstring 15 may also include any suitable combination of peripheralelements (e.g., fiber optic cable connectors, splitters, etc.) wellknown in the art for coupling the fibers. Further, the fibers may beencased in protective coatings, and may be deployed in fiber deliveryequipment, as is also well known in the art.

In the embodiments employing fiber optic sensors, fiber optic pressuresensors described in U.S. Pat. No. 6,016,702, entitled “High SensitivityFiber Optic Pressure Sensor for Use in Harsh Environments” and issued toMaron on Jan. 25, 2000, which is herein incorporated by reference in itsentirety, as well as any pressure sensors described in U.S. Pat. No.5,892,860, entitled “Multi-Parameter Fiber Optic Sensor for Use in HarshEnvironments” and issued to Maron et al. on Apr. 6, 1999, which isherein incorporated by reference in its entirety, may be utilized. Thedifferential pressure sensor may include any of the embodimentsdescribed in U.S. patent application Ser. No. 10/393,557, entitled“Optical Differential Pressure Transducer Utilizing a Bellows andFlexure System,” filed by Jones et al. on Mar. 21, 2003, which is hereinincorporated by reference in its entirety. Any of the fiber opticpressure sensors described in the above-incorporated patents or patentapplications is suitable for use with the present invention as thesensors placed within the differential pressure sensor 50 or as absolutepressure sensors 70 and 75.

In all of the above embodiments, multiple inverse Venturi meters 60having diverging inner diameters at the throat 61 may be employed alongthe tubing string 15 to monitor flow rates at multiple locations withinthe wellbore 20. The inverse Venturi meter 60 of the above embodimentsmay be symmetric or asymmetric in shape across the throat 61, dependingupon the divergence angles X and Y and the corresponding lengths ofportions 60B and 60C.

While the foregoing is directed to embodiments of the present invention,other and further embodiments of the invention may be devised withoutdeparting from the basic scope thereof, and the scope thereof isdetermined by the claims that follow.

1. An apparatus for measuring a flow rate of a fluid flowing in a pipe,comprising: a divergent differential pressure sensor disposed along thepipe for sensing differential pressure across first and second locationsalong the pipe, wherein the first location is at a portion of the pipehaving an enlarged inner diameter, and wherein the pipe diverges from anominal inner diameter of the pipe where the second location is to theenlarged inner diameter of the pipe in the direction of fluid flow;processing equipment capable of determining the flow rate of the fluidusing differential pressure information from the differential pressuresensor and a density of the fluid without further fluid relatedinformation input into the processing equipment; and one or moretransmission lines for communicating the differential pressureinformation from the differential pressure sensor to the processingequipment.
 2. The apparatus of claim 1, wherein the differentialpressure sensor is capable of detecting a measurable pressuredifferential of 0.001 psid.
 3. The apparatus of claim 1, wherein theprocessing equipment comprises logic configured to calculate the flowrate based on the differential pressure and the density of the fluid. 4.The apparatus of claim 3, wherein the logic is further configured tocalculate the density of the fluid proximate the first and secondlocations.
 5. The apparatus of claim 1, wherein the processing equipmentis configured to perform an operation, comprising:${Q = \sqrt{\frac{2}{\rho} \times {DP} \times \frac{\pi}{4} \times \left\lbrack {D_{B}^{2} - D_{A}^{2}} \right\rbrack}},$where Q=the flow rate, p=a density of the fluid, DP=the differentialpressure, D_(B)=the enlarged inner diameter, and D_(A)=the nominal innerdiameter.
 6. The apparatus of claim 1, wherein a minimum measurable flowrate using the differential pressure sensor is approximately 0.08 feetper second.
 7. A method for determining the flow rate of fluid throughdownhole tubing, comprising: locating the downhole tubing in a wellbore,wherein an enlarged inner diameter portion of the downhole tubing isdisposed upstream of a remaining portion of the tubing; measuring apressure differential between the enlarged inner diameter portion of thetubing and the remaining portion of the tubing; and determining the flowrate of the fluid using the pressure differential wherein determiningthe flow rate occurs without relying on further fluid pressure relatedinformation other than the pressure differential.
 8. The method of claim7, wherein the pressure differential is measured by a differentialpressure sensor coupled to the tubing.
 9. The method of claim 8, furthercomprising measuring a density of the fluid.
 10. The method of claim 7,wherein the pressure differential is measured by determining adifference between the pressure measured by at least two absolutepressure sensors, a first absolute pressure sensor located proximate theenlarged inner diameter portion and a second absolute pressure sensorlocated proximate the remaining portion.
 11. An apparatus for measuringflow rate of fluid within a wellbore, comprising: a tubing stringdisposed in the wellbore and having a diverging inner diameter portionpositioned upstream of a section of the tubing string; and a singledivergent differential pressure sensor disposed on a flow measuringsection of the tubing string and the diverging inner diameter portionfor measuring a difference between fluid pressure in the section of thetubing string and fluid pressure in the diverging inner diameterportion, wherein only the single divergent differential pressure sensorsenses pressure of the fluid in the flow measuring section.
 12. Theapparatus of claim 11, wherein the differential pressure sensor has adifferential pressure resolution of 0.001 psid.
 13. The apparatus ofclaim 11, further comprising a processing system connected to thedifferential pressure sensor for converting measurements of thedifferential pressure sensor to flow rate data using a density of thefluid.
 14. The apparatus of claim 13, wherein the processing equipmentis configured to perform an operation, comprising:${Q = \sqrt{\frac{2}{\rho} \times {DP} \times \frac{\pi}{4} \times \left\lbrack {D_{B}^{2} - D_{A}^{2}} \right\rbrack}},$where Q=the flow rate, ρ=a density of the fluid, DP=the differencebetween fluid pressure, DB=an inner diameter at the diverging innerdiameter portion, and D=an inner diameter of the section of the tubingstring.